Boring tool tracking fundamentally based on drill string length, pitch and roll

ABSTRACT

A boring tool moves having a pitch orientation, a yaw orientation and a roll orientation and is steerable underground using the roll orientation. A maximum drill string curvature is established for steering. The boring tool is advanced over a path segment. An averaged roll characteristic is determined for movement of the boring tool along the path segment. A path segment pitch orientation is established based on at least one measured pitch orientation along the path segment. Using the maximum drill string curvature in combination with the averaged roll characteristic and the path segment pitch orientation, the yaw orientation is determined. The averaged roll characteristic is determined based on a series of incremental roll measurements that are spaced across the path segment. A set of coupled ordinary differential equations is used to characterize movement of the boring tool.

This application is a continuation application of copending applicationSer. No. 13/688,314 filed Nov. 29, 2012; which is a continuationapplication of Ser. No. 13/422,690 filed Mar. 16, 2012 and issued asU.S. Pat. No. 8,342,262 on Jan. 1, 2013; which is a continuationapplication of Ser. No. 13/151,517 filed Jun. 2, 2011 and issued as U.S.Pat. No. 8,157,023 on Apr. 17, 2012; which is a continuation applicationof Ser. No. 12/780,421 filed May 14, 2010 and issued as U.S. Pat. No.7,967,080 on Jun. 28, 2011; which is a continuation application of Ser.No. 12/325,182 filed Nov. 29, 2008 and issued as U.S. Pat. No. 7,743,848on Jun. 29, 2010; which is a continuation application of Ser. No.11/930,483 filed Oct. 31, 2007 and issued as U.S. Pat. No. 7,472,761 onJan. 6, 2009; which is a continuation application of Ser. No. 11/609,786filed Dec. 12, 2006 and issued as U.S. Pat. No. 7,306,053 on Dec. 11,2007; which is a continuation application of Ser. No. 11/051,878 filedFeb. 5, 2005 and issued as U.S. Pat. No. 7,165,632 on Jan. 23, 2007;which is a continuation application of Ser. No. 10/341,922 filed Jan.13, 2003 and issued as U.S. Pat. No. 6,868,921 on Mar. 22, 2005; thedisclosures of which are incorporated herein by reference.

The present invention relates generally to the field of directionaldrilling and, more particularly, to a directional drilling system whichprovides for tracking of a boring tool fundamentally requiring no morethan pitch and roll measurements as measured parameters. In one feature,measurement error compensation is accomplished using a Kalman filterwithin the framework of a heretofore unseen set of coupled ordinarydifferential equations.

BACKGROUND OF THE INVENTION

A boring tool, or other such underground object, is characterized in adrilling region by six unknown parameters comprising a location in threedimensional space, described using some form of coordinates, andorientation parameters that are generally referred to as pitch, roll andyaw. The former two orientation parameters are rather readily measurablein a direct way, as is typically accomplished in the prior art, by usingsensors that are positioned within the boring tool for movementtherewith. The yaw orientation parameter, however, is considerably moredifficult to determine in the context of prior art techniques, as willbe discussed below. Moreover, direct measurement of yaw using, forexample, a magnetometer in the boring tool is more problematic thandirect measurement of pitch and roll orientation which can be performedwith relatively simple mechanical type sensors or based onaccelerometers readings. A particular problem resides in such direct yawmeasurements being prone to significant levels of measurement error inthe presence of magnetic interference.

One class of prior art, as exemplified by U.S. Pat. No. 5,764,062(hereinafter the '062 patent), entitled TECHNIQUE FOR ESTABLISHING ANDRECORDING A BORING TOOL PATH USING A SURVEY REFERENCE LEVEL, simplyignores yaw as an unknown for purposes of position determination. Thatis, all remaining parameters are integrated to track the undergroundposition of the boring tool.

More recently, another class of system has been developed which accountsfor yaw orientation. U.S. Pat. No. 6,035,951 (hereinafter the '951patent), entitled SYSTEMS, ARRANGEMENTS AND ASSOCIATED METHODS FORTRACKING AND/OR GUIDING AN UNDERGROUND BORING TOOL, which is commonlyassigned with the present application and hereby incorporated byreference, serves as a sophisticated, robust example of such a system.While this system provided remarkable and sweeping advantages over thethen-existing prior art and continues to be highly effective, onefeature is shared with the prior art respecting determination of yaworientation. Specifically, an electromagnetic locating signal istransmitted from the boring tool which is measured at one or more aboveground locations. The measurement of the locating signal thencontributes in a direct manner to the determination of yaw orientation.At least in a general sense, the prior art has accepted the precept thatmeasurement of electromagnetic flux is a preferred way to resolve yaworientation.

The present invention accounts for yaw in all of its various forms and,at the same time, sweeps aside the foregoing precept of the prior art ina highly advantageous manner while providing still further advantages.

SUMMARY OF THE INVENTION

As will be described in more detail hereinafter, there is disclosedherein an arrangement and associated method for use in tracking and/orguiding the movement and an overall orientation of an underground boringtool, characterized by a pitch orientation and a roll orientation, in aregion of ground. In one aspect of the present invention, thearrangement is used as part of a system such that the boring tool issteerable underground using the roll orientation. The boring tool may beadvanced using a drill string which exhibits a maximum drill stringcurvature in the region. The boring tool is configured for advancing ina straight ahead mode during a continuous roll and is further configuredfor advancing in a steering mode by moving the boring tool at a fixedroll orientation. The boring tool is advanced over a path segment in theregion using at least one of the straight ahead mode and the steeringmode. An averaged roll characteristic is determined for movement of theboring tool along the path segment. A path segment pitch orientation isdetermined based on at least one measured pitch orientation of theboring tool along the path segment. Using the maximum drill stringcurvature in combination with the averaged roll characteristic and thepath segment pitch orientation, the yaw orientation of the boring toolis determined. In one feature, the boring tool is advanced through aseries of positions that are spaced across the path segment, separatedby an at least generally equal increment for measuring a series of rollpositions of the boring tool and the averaged roll characteristic isestablished using the measured series of roll positions. Accordingly,determination of yaw orientation can be based in a fundamental way onpitch and roll orientation measurement. In another feature, the need forusing the maximum path curvature in the yaw orientation determination iseliminated by requiring that movement of the boring tool over the pathsegment exhibits a significant vertical component of movement.

In another aspect of the present invention, the boring tool is advancedover a path segment having a vertical component of motion in the regionusing at least the steering mode. An averaged roll characteristic of theboring tool is established for the path segment. A path segment pitchorientation is determined based on at least one measured pitchorientation of the boring tool along the path segment. Using theaveraged roll characteristic and the path segment pitch orientation, theyaw orientation of the boring tool is determined. In accordance withthis aspect of the present invention, determination of maximum pathcurvature is not required.

In still another aspect of the present invention, a system is describedfor tracking a boring tool which may be advanced in an undergroundregion responsive to a drill string. The boring tool exhibits an overallorientation that is characterized by a pitch orientation, a yaworientation and a roll orientation, and is steerable underground in theregion using the roll orientation. The boring tool is configured foradvancing in a straight ahead mode during a continuous roll and furtherfor advancing in a steering mode by moving the boring tool at a fixedroll orientation. The boring tool is advanced over a series of pathsegments, each of which includes a start position and an end position,using at least one of the straight ahead mode and the steering modeduring each path segment. Each path segment includes a segment lengthsuch that the start position of each successive one of the path segmentscoincides with a last-determined end position within the series of pathsegments. An incremental change in the pitch orientation and anincremental change in the yaw orientation of the boring tool over acurrent one of the path segments are determined based, at least in part,on a series of roll measurements that are taken during the current pathsegment for use in tracking the boring tool over the current pathsegment. In one feature, the incremental change in the pitch orientationand the incremental change in the yaw orientation for the current pathsegment are determined by determining a maximum path curvature of thedrill string in the region for a fixed roll orientation of the boringtool in the steering mode. A set of data is measured relating to aseries of roll positions of the boring tool at a corresponding series ofpositions that are spaced across the current path segment, separated byan at least generally equal increment, as the boring tool advancesthrough the current path segment. Thereafter, the incremental change inthe pitch orientation and the incremental change in the yaw orientationare established using the set of data in combination with the maximumcurvature of the drill string. In another feature, extrapolation isperformed from the start position of the current path segment todetermine a predicted location of its end position and to determine apredicted overall orientation at its end position based, at least inpart, on (i) the last-determined end position, (ii) the incrementalchange in the pitch orientation and (iii) the incremental change in theyaw orientation. A current path segment pitch orientation is determinedusing at least one measured pitch orientation of the boring tool takenalong the current path segment. The predicted location and predictedoverall orientation for the end position of the current path segment arecorrected, based at least in part on the current path segment pitchorientation, to resolve a corrected location of the boring tool whichmore accurately tracks the end position of the current path segment. Instill another feature, a current path segment yaw orientation isdetermined using at least one measured yaw orientation of the boringtool taken along the current path segment and the correction uses thecurrent path segment yaw orientation in combination with the currentpath segment pitch orientation to resolve the corrected location of theboring tool.

In one technique of the present invention, the boring tool includesmeans for transmitting an electromagnetic locating signal which behavesconsistently with a set of electromagnetic equations and the systemincludes means for measuring the electromagnetic locating signal at oneor more receiving locations to produce a measured set of electromagneticreadings. The set of electromagnetic readings is measured at the endposition of the current path segment and the aforementionedextrapolation determines a predicted set of the electromagnetic readingsat the end position. A correction procedure compares the predicted setof electromagnetic readings for the end position of the current pathsegment to the measured set of electromagnetic readings to furtherresolve the corrected location of the boring tool. In one feature, acurrent path segment yaw orientation is determined using at least onemeasured yaw orientation of the boring tool taken along the current pathsegment and the correction procedure uses the current path segment yaworientation, the current path segment pitch orientation and a comparisonof the predicted and measured sets of electromagnetic readings toenhance the corrected position of the boring tool.

In yet another aspect of the present invention, a system is describedfor tracking a boring tool which moves in an underground region havingan overall orientation that is characterized by a pitch orientation, aroll orientation and a yaw orientation. A set of coupled ordinarydifferential equations is used to characterize a rate of change of atleast the pitch orientation and the yaw orientation of the boring toolas well as a position of the boring tool in the region. With movement ofthe boring tool in the region, the set of coupled ordinary differentialequations is integrated to track a predicted overall orientation and apredicted position of the boring tool. In one feature, one or moremeasured parameters are used during progression of the boring tool toenhance accuracy of the predicted overall orientation and the predictedposition of the boring tool. In another feature, the one or moremeasured parameters are used in a corrector step of a Kalman filter.

In a continuing aspect of the present invention, a system is describedfor tracking a boring tool which moves in an underground region havingan overall orientation that is characterized by a pitch orientation, ayaw orientation and a roll orientation, and which is steerableunderground in the region using the roll orientation. The boring tool isconfigured for advancing in a straight ahead mode during a continuousroll applied by the drill string and is further configured for advancingin a steering mode by moving the boring tool at a fixed roll orientationapplied by the drill string. A set of initial parameters is establishedat a first position of the boring tool including at least an initialpitch orientation and an initial yaw orientation. The boring tool isadvanced over a first segment from the first position to a secondposition in the region using at least one of the straight ahead mode andthe steering mode to establish a nominal path while measuring a segmentlength of the first segment. An incremental change in the pitchorientation and an incremental change in the yaw orientation of theboring tool are established over the first segment. Extrapolation isperformed from the first position to determine a predicted location ofthe second position and to determine a predicted overall orientation atthe second position based, at least in part, on (i) the set of initialparameters, (ii) the incremental change in the pitch orientation, (iii)the incremental change in the yaw orientation and (iv) the measuredsegment length. A path segment pitch orientation is determined using atleast one measured pitch orientation of the boring tool along the pathsegment. The predicted location and predicted overall orientation at thesecond position are determined, based at least in part on the pathsegment pitch orientation, to resolve a corrected location of the boringtool which more accurately characterizes the second position.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be understood with reference to the detaileddescription taken in conjunction with the drawings briefly describedbelow.

FIG. 1 is a diagrammatic view, in elevation, of a drilling system thatis produced in accordance with the present invention and shown here toillustrate details with respect to its operation including referencepositions along a drill path of the boring tool.

FIG. 2 is a diagrammatic plan view of the system of FIG. 1 showingfurther details of the drill path.

FIG. 3 is a diagrammatic perspective view of a boring tool showing itsorientation in a global coordinate system and in a transmittercoordinate system, as well as showing pitch and yaw orientation of theboring tool.

FIG. 4 is another diagrammatic perspective view of the boring tool ofFIG. 3 showing further details with respect to orientation parametersused herein including a relationship between yaw in transmittercoordinates versus yaw in global coordinates with respect to pitch axesthat are angularly skewed by the pitch of the boring tool.

FIG. 5 a is a diagrammatic plot, in the x-y plane, of an assumed drillpath and above ground receivers that are positioned proximate theretofor use in a simulation for purposes of validation of technique A,wherein predicted positions of the boring tool are shown as “+” symbolsproximate to the solid line of the assumed path.

FIG. 5 b is a dual plot against arc length s of the drill path showingerror in x and y positional coordinates for the predicted positions ofFIG. 5 a.

FIG. 5 c shows a coordinate surface defined by the vertical, z axis andarc length s, illustrating further details of the assumed path of FIG. 5a including vertical movement of the boring tool on the assumed path.

FIG. 5 d is a plot of z axis error for the predicted data of FIG. 5 calong arc length s.

FIG. 5 e is a plot of pitch against arc length s showing actual pitchorientation along the assumed path as well as “measured” or“synthesized” pitch values, exhibiting introduced measurement error,that are used in the technique A simulation.

FIG. 5 f is a plot of two types of pitch error against arc length sincluding introduced measurement error for synthesized pitch sensorreadings taken by the boring tool along the assumed path where eachpitch measurement error value is indicated as a circle and including aplot of prediction error in the pitch value along s as determined bytechnique A and influenced by the measurement error.

FIG. 5 g shows exact yaw orientation of the assumed path, as a solidline, and predicted yaw orientations, shown as “+” symbols, plottedagainst arc length s wherein the predicted yaw values are produced bytechnique A.

FIG. 5 h shows yaw error plotted against s for the predicted yaw valuesof FIG. 5 g.

FIGS. 6 a and 6 b show error estimates for the assumed path defined as 1standard deviation or 1 sigma, obtained from exact cone fluxes and pitchand representing errors in position coordinates (FIG. 6 a), as well aspitch and yaw angles (FIG. 6 b) that can be expected using measuredfluxes and pitch as input for the tracking technique.

FIG. 7 a illustrates pitch and yaw orientation along an assumed drillpath, plotted as solid lines against the x axis, for use in a simulationwhich employs technique D of the present invention and which furtherillustrates synthesized “measured” pitch and roll values, that are usedas input for the simulation.

FIG. 7 b is a plan view plot, in the x-y coordinate plane, of theassumed path of FIG. 7 a, further showing technique D predicted x-ypositions for the assumed path of the boring tool.

FIG. 7 c is a plot of the yaw angle of the assumed path of FIGS. 7 a and7 b against the x axis, further showing technique D calculated yawvalues as “+” symbols.

FIG. 7 d is a plot of boring tool depth in the x-z coordinate planeshowing the depth of the assumed path of FIGS. 7 a and 7 b as well astechnique D predicted depth values which are indicated as “+” symbols.

FIG. 8 is a flow diagram of technique B illustrating a step-by-stepsolution of drillpath variables.

DETAILED DESCRIPTION OF THE INVENTION

Turning now to the figures wherein like components are indicated by likereference numbers throughout the various figures, attention isimmediately directed to FIG. 1 which diagrammatically illustrates ahorizontal directional drilling system generally indicated by thereference number 10 and produced in accordance with the presentinvention. It is noted that the figures are not to scale for purposes ofillustrative clarity and that like reference numbers refer to likecomponents wherever possible throughout the various figures. FIG. 1 isan elevational view of system 10 operating in a region 12. System 10includes a drill rig 14 having a drill string 16 extending therefrom toa boring tool 20. The drill string is pushed into the ground to moveboring tool 20 at least generally in a forward direction 22 indicated byan arrow.

In the illustrated technique of system 10, a locating signal 30 istransmitted from the boring tool to receivers R1 and R2 positioned onthe surface of the ground. It is to be understood, however, that neitherlocating signal 30 nor receivers R1 and R2 are required, as will bedescribed in detail at an appropriate point below. In techniques whichemploy the use of a locating signal and associated receivers, however,and as is described in the above incorporated '951 patent, the positionof the boring tool may be determined, at least in part, based uponcertain characteristics of locating signal 30 at R1 and R2. In anyimplementation of the present invention using an electromagneticlocating signal, measurement of the locating signal produces a set ofelectromagnetic readings that is used to further resolve a predictedposition and orientation of the boring tool within region 12. Thelocation of the boring tool within region 12 as well as the undergroundpath followed by the boring tool may be established and displayed atdrill rig 14, for example, on a console 40. Information is transmittedfrom R1 and R2 to the drill rig via telemetry signals T1 and T2,respectively. In addition, information regarding certain parameters ofthe boring tool such as, for example, pitch and roll (orientationparameters) and temperature are encoded onto locating signal 30 duringdrilling, for receipt by R1 and R2. These parameters may be measured bya suitable sensor arrangement 41 located within the boring tool whichmay include, for example a pitch sensor, a roll sensor and, in certainimplementations, a yaw sensor such as a magnetometer. After encoding,the information is thereafter transmitted to drill rig 14 via T1 and T2,for receipt by an antenna 42 at the drill rig. Along with the drillingpath, any parameter of interest in relation to drilling such as, forexample, pitch may be displayed on display 40.

Referring to FIG. 2 in conjunction with FIG. 1, drill string 16 issegmented, being made up of a plurality of removably attachable,individual drill pipe sections having a section or segment length. Thedrill pipe sections may be referred to interchangeably as drill rodshaving a rod length. During operation of the drill rig, one drill pipesection at a time is pushed into the ground by the drill rig using amovable carriage 44. Drill rig 14 may include any suitable arrangementfor measuring movement of the drill string into the ground such as isdescribed, for example, in the above incorporated '951 patent. As willbe seen, movement of the drill pipe into the ground by an incrementalamount may trigger measurements of certain orientation parameters of theboring tool. Other orientation parameters may be measured moreintermittently. For example, measurements can be made responsive tocompletion of pushing each drill pipe section into the ground. Stillfurther measurements may be made upon completing and/or starting a newdrill pipe section. In this regard, positions k of the boring tool,where k=0, 1, 2, etc. is an integer indicative of a particular position,correspond to a plurality of positions through which the boring tool issteered and at each of which a new drill pipe section is added to thedrill string. With regard to the drill string, particularly inconsideration of those techniques of the present invention which do notrequire transmission of a locating signal, it is important to understandthat any data and/or parameters measured at the boring tool may betransferred to the drill rig through the drill string. Highlyadvantageous systems for accomplishing such a transfer using a segmenteddrill string are described in commonly assigned U.S. Pat. No. 6,223,826,entitled AUTO-EXTENDING/RETRACTING ELECTRICALLY ISOLATED CONDUCTORS IN ASEGMENTED DRILL STRING, as well as copending U.S. application Ser. Nos.09/793,056 and 09/954,573, all of which are incorporated herein byreference.

A number of techniques, referred to herein as A to D, are described fortracking position and pointing direction of an underground drill head.One element of techniques A, B and C is data processing employing aKalman filter in order to minimize the effect of data measurementerrors, although it is to be understood that any other suitabletechnique for minimization of such errors such as, for example, a leastsquares approach is equally applicable. Techniques A and B require atleast one tri-axial antenna cluster (at least one of R1 and R2) for themeasurement of locating field 30. These antenna clusters, which may bereferred to as cones in this disclosure, may be installed above or belowthe ground surface. Any number of cones can be handled withoutmodifications. Another important new feature that remains to bedescribed in this disclosure is the formulation of a set of coupledfirst-order ordinary differential equations, referred to as rodequations, suited for tracking a drill head (boring tool) underrealistic drilling conditions in one unified approach. These rodequations are considered to be highly advantageous, in and bythemselves, and Applicants are unaware of their existence heretofore.

NOMENCLATURE

The various equations described below and in the figures utilize thefollowing nomenclature:

-   -   b_(x), b_(y), b_(z)=components of flux for unit dipole strength        in a global or overall local coordinate system defined in the        drilling region    -   F=continuous state equations matrix    -   H=observation coefficient matrix    -   N=number of roll angles measured along a distance Δs    -   P=error covariance matrix    -   Q=continuous process noise covariance parameter matrix    -   Q_(k)=discrete process noise covariance matrix    -   R=observation covariance matrix    -   sin θ, cos θ=steering/drilling parameters    -   s=arc length along rod axis    -   {right arrow over (x)}=(δx, δy, δz, δκ, δφ, δζ, state variables        vector    -   x, y, z=global coordinates, origin at drill begin    -   x, y, z=coordinates parallel to global, origin at center of        transmitter    -   {right arrow over (z)}=measurement vector    -   β=yaw angle, rotation about {right arrow over (z)}-axis    -   δx, δy, δz=position state variables    -   δκ, δφ, δζ=curvature, pitch and yaw state variables    -   Δs=rod length increment    -   φ=pitch angle    -   Φ_(k)=discrete state equation transition matrix    -   κ=maximum drill path curvature    -   θ=roll angle    -   σ=standard deviation    -   σ⁻²=variance, square of standard deviation    -   ζ=yaw angle, rotation about transmitter z_(r)-axis

Subscripts

-   -   k k-th position on drill path    -   m measured    -   t transmitter coordinates

Superscripts

-   -   ( )′ transpose    -   ( )* nominal drill path    -   ( )⁻ last available estimate    -   {dot over (()}{dot over ( )} derivative d/ds {right arrow over        ({circumflex over (x)} state variables estimate

Components for Implementations of Tracking System Techniques

Each technique requires different equipment combinations for drill headtracking, as summarized in Table 1.

TABLE 1 Component Technique A Technique B Technique C Technique DTransmitter magnetic Yes Yes No No dipole generator pitch sensor Yes YesYes Yes roll sensor Yes Yes Yes Yes yaw sensor No Yes * No Cones Yes YesNo No Rod length Yes Yes Yes Yes measuring device * Indicates optionalcomponents, as described in further detail below.

As a general summary of the information in Table 1, techniques A and Bemploy the tracking system illustrated in FIGS. 1 and 2 to monitor theposition of the boring tool. This system features one or more stationarycones either above or below the ground surface and associated dataacquisition and processing capability. Each cone contains a cluster oftri-axial antennas for flux measurements. In addition, the cones areequipped with sensors to measure their angular orientation with respectto a “global” coordinate system. It is to be understood that the extentsof this coordinate system need be global only in terms of covering theentirety of the drilling region of interest and is, therefore, intendedonly as designating a “senior” measurement framework assigned within thelocal region. Of course, the term “coordinate system”, as used herein,is defined broadly as merely a convenient construction for referencingphysical world locations in descriptive terms. The position coordinatesof all cones are recorded before drilling begins. An unlimited number ofcones can be handled by the described techniques without modification.Furthermore, techniques A and B require a transmitter designed togenerate a magnetic dipole field from the boring tool andinstrumentation to measure pitch and roll orientation of the boringtool. The need for a yaw measurement device in the boring tool dependson the choice of tracking technique. It is noted that techniques C and Dare suited for use in a more minimalistic tracking system, as comparedto the robust techniques A and B, since these techniques do not rely onthe measurement of a magnetic field generated from the boring tool.

All of these techniques require measurements of drill rod length changesin a suitable manner such as, for example, by using a potentiometer orultrasonic sensor such as described in the '951 patent. For someapplications where rod length does not vary much during the bore and amore limited tracking accuracy is sufficient, a simple counter for thenumber of drill rods and measurement of a nominal rod length can besubstituted.

Measured Data

Measured data required as input for the tracking techniques are listedbelow. Note that techniques A, B, C and one version of implementation Drequire an estimate of the maximum rod curvature achievable during puresteering where the drill head is pushed into the soil while keeping itsroll position unchanged. This curvature must either be known fromprevious steering with the same equipment in similar soil or could beobtained from a preliminary test measuring the change of pitch angle Δφover one rod length l_(rod) with the drillhead in the 12 o'clock rollposition. Maximum curvature is then given by κ=Δφ/l_(rod).

Measured Data in Techniques A and B

-   -   Fluxes b_(x), b_(y), b_(z) at each cone for unit dipole strength    -   Rod length increment Δs    -   Transmitter pitch angle φ    -   Transmitter yaw angle β (method B only)    -   Transmitter roll angle θ at N equal intervals along Δs    -   Maximum rod curvature κ achievable during steering at a fixed        roll angle

Measured Data in Techniques C and D

-   -   Rod length increment Δs    -   Transmitter pitch angle φ    -   Transmitter yaw angle β (technique C only)    -   Transmitter roll angle θ at N equal intervals along Δs    -   Maximum rod curvature κ achievable during steering at a fixed        roll angle (only for one version of technique D)

Definitions for Drilling and Steering

In horizontal directional drilling, three different types of drillingtechniques are in use to achieve a desired drill path. In thisdisclosure, these drilling techniques are referred to as “drilling”,“steering”, and, for lack of a better term, “alternatedrilling/steering”. The boring tool features a drill bit designed suchthat a pure rotating motion (“drilling”) will form a straight drill pathin a homogeneous soil. Positioning the drill bit at a fixed roll angle(“steering”) allows steering along a curved drill path that has themaximum achievable (i.e., tightest) rod curvature during steering.Rotation and thereby roll orientation control of the boring tool may beaccomplished in at least two ways: first, the drill string itself may berotated by the drill rig with the boring tool attached thereto; second,the boring tool may be rotated at the end of the drill string using asuitable motor arrangement such as, for example, a drill mud poweredhydraulic motor or an electric motor that is powered through the drillstring. Maximum curvature depends on drill bit design, soil conditions,drill rod dimensions, rod bending characteristics and drill mud. Theuser can alternate between drilling and steering along a rod (“alternatedrilling/steering”) to move the tool along a drill path with lesscurvature. All tracking techniques described herein are able to accountfor steering, drilling and such a mixed mode of operating the boringtool in one unified analysis.

Assuming roll angle θ of the boring tool is measured N times at equalintervals along a section Δs of the drill rod (for example, from k=0 tok=1 in FIG. 1). These roll measurements may be made on-the-fly, as thedrill string advances in the ground. The following roll parameters aredefined where the overbar indicates an average value.

$\begin{matrix}{\overset{\_}{\sin \; \theta} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{\sin \; \theta_{i}}}}} & (1) \\{\overset{\_}{\cos \; \theta} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{\cos \; \theta_{i}}}}} & (2)\end{matrix}$

In essence, these expressions represent a set of data that is determinedbased on roll measurements that are taken at the spaced apartincremental positions. It is recognized that both sin θ and cos θ go tozero for a given distance with a constant rate of roll and a pluralityof measurements of roll angle taken at equally spaced apart incrementsalong the given distance. The number of measurement positions should besufficient to characterize the roll motion of the boring tool over thesegment of the boring tool to a suitable approximation. For example, twomeasurements is considered to be insufficient, while a measurement everysix inches along the segment is considered to be suitable. As anotherexample, one hundred measurements for a drill rod having a length of tenfeet is satisfactory, of course, accuracy generally increases withincreasing numbers of measurements. The number of roll measurements maybe based on system limitations including sensor limitations andprocessing power. That is, any system exhibits some minimum measurementtime that is required to perform a roll measurement. Accordingly, thenumber of roll measurements, contributing to the results of equations 1and 2, may be maximized based on this system determined minimum rollmeasurement time. The definitions of equations 1 and 2 correspond to theaveraged sine and cosine of the roll angles and allow for clearlydistinguishing between drilling, steering, and alternatedrilling/steering on the basis of a steering parameter

$\sqrt{\overset{\_}{\sin \; \theta^{2}} + \overset{\_}{\cos \; \theta^{2}}}.$

This parameter is equal to zero for straight ahead drilling, one forsteering at a constant roll angle and assumes intermediate values foralternate drilling/steering.

Governing Equations

Referring to FIGS. 3 and 4, for purposes of illustrating therelationships among the variables, the following set of differentialequations, termed rod equations in this disclosure, describes the pathof a boring tool for drilling, steering and alternate drilling/steering.All techniques described herein rely on these equations.

{dot over (x)}=cos β cos φ  (3)

{dot over (y)}=sin β cos φ  (4)

ż=sin φ  (5)

{dot over (κ)}=0  (6)

{dot over (φ)}=κ cos θ  (7)

{dot over (ζ)}=−κ cos θ  (8)

Here, arc length s, measured along the drill rod axis including itscurvature, is chosen to be an independent variable. The superscript dotdenotes derivatives with respect to s. The variables x, y, z denotedrill path coordinates in the aforementioned global system with a globalorigin 50 at the point of drill begin (position k=0 in FIGS. 1 and 2).The symbol κ denotes the maximum drill rod curvature that is onlyachievable with pure steering at a constant or fixed roll angle. Thiscurvature is approximately constant along the length of the bore as longas soil conditions and steering effectiveness are unchanged. The symbolφ represents pitch angle (positive “nose up”), as is illustrated.

The analysis employs two different yaw angles, termed β and ζ. Angle βis the rotation angle about the z axis (parallel to the global z axis),defined positive counterclockwise when looking down onto the groundsurface, as can be seen in the perspective view of FIG. 3. Thenomenclature x_(t), y_(t) and z_(t) denotes a set of orthogonal axesthat move with boring tool 20 having axis x_(t) coinciding with anelongation axis of the boring tool, axis y_(t) is normal to x_(t) andhorizontal, and z_(t) is normal to the x_(t), y_(t) plane. In theinstance where system 10 uses a locating signal, the origin of thex_(t), y_(t), z_(t) coordinate system coincides with the origin oflocating signal 30 which is generally arranged at some point along anelongation axis of the boring tool. Yaw angle ζ arises from a rotationabout the z_(t)axis. FIG. 3 illustrates the following relationshipbetween the two types of yaw rotations.

{dot over (ζ)}={dot over (β)} cos φ  (9)

That is, the rate of change in ζ is directly related to the rate ofchange in β by the cosine of φ. In addition to the rod equations,well-known equations describing the field of a three-dimensionalmagnetic dipole are utilized. These dipole equations are givenimmediately below for the reader's convenience:

(b _(y) ,b _(y) ,b _(z))′=3x _(s) r ⁻⁵ {right arrow over (r)}−r ⁻³{right arrow over (t)} ₁  (10)

x _(s) ={right arrow over (t)} ₁ ′·{right arrow over (r)}  (11)

{right arrow over (r)}=(x _(c) −x,y _(c) −y,z _(c) −z)′  (12)

{right arrow over (t)} ₁=(cos β cos φ, sin β cos φ, sin φ)′  (13)

The dipole equations provide the flux induced by a three-dimensionalmagnetic dipole of unit strength at a cone positioned at(x_(c),y_(c),z_(c)). Here, the superscript “prime” indicates thetranspose of a vector.

Attention is now directed to specific details of each of trackingtechniques A-D, beginning with tracking technique A.

Tracking Technique A

The posed problem is an initial value problem for determining drill pathparameters x, y,z,κ,φ,ζ. Rod equations 3-8 and magnetic dipole equations10-13 are solved, taking measured pitch and magnetic fluxes intoaccount. Drilling begins at the origin of the global coordinate system(FIGS. 1 and 2, position k=0) where values of curvature, pitch and yawangles must be known, the latter two for example, through sensors. Itshould be appreciated that any position may serve as a starting positionfor initiation of the procedure so long as these values can bedetermined. Furthermore, an estimate of the expected accuracy of initialvalues of all drill path parameters must be available to form the Kalmanfilter error covariance matrix P₁. All elements of P₁ are zero exceptfor the three diagonal variances σ_(κ) ₁ ², σ_(φ) ₁ ², σ_(ζ) ₁ ²representing the accuracy of κ₁, φ₁, ζ₁.

Starting with these known initial values at drill begin (k=0), the setof rod equations is integrated along the drill path. Having determinedall drill path parameters at the k-th position and measuring pitch andfluxes at all cones with the transmitter at the next, (k+1)-st position,the parameters of this new position are obtained in three steps, asfollows:

Step 1: A location on a nominal drill path is determined by quadraticextrapolation from the last known position. The nominal drill path is acircular arc from the k-th to the (k+1)-st position, defined by thevariables x*, y*, z*, κ*, φ*, β*. The analysis starts with an estimateof the change of pitch and yaw angles, Δφ, Δζ, along the rod lengthelement Δs determined from rod equations (2e) and (2f). While thepresent description uses the drill pipe section (or rod length) as Δs,it is to be understood that any suitable length may be used as analternative in view of the teachings herein.

Variables defining the nominal drill path at the (k+1)-st drill pathposition depend on known values at the k-th position and on Δφ and Δζ.Quadratic extrapolation can be performed, for example, applyingpublished mathematical techniques such as the one of J. W. Burrowstitled “Mathematics of Strapdown Inertial Navigation”, InternationalCongress on Industrial and Applied Mathematics (ICIAM), 1987. Havingdetermined the nominal drill path, magnetic fluxes emitted by atransmitter on this path can be calculated at each cone position usingdipole equations 10-13.

Step 2: Employing Kalman filter analysis procedure, equations governingstate variables are derived by linearizing rod equations 3 through 8.State variables, used herein, comprise differences between the nominaldrill path and the final drill path, as predicted by Kalman filteranalysis, for position coordinates x, y, z, curvature κ, pitch φ and yawβ or ζ. State variables and their governing continuous state equationsread

$\begin{matrix}{\overset{->}{x} = \left( {{\delta \; x},{\delta \; y},{\delta \; z},{\delta \; \kappa},{\delta \; \varphi},{\delta \; \zeta}} \right)^{\prime}} & (14) \\{{\overset{\overset{->}{.}}{x} = {{F\; \overset{->}{x}} + \overset{->}{u}}}{{{with}\mspace{14mu} F} = \begin{bmatrix}0 & 0 & 0 & 0 & {{- \cos}\; {\beta sin}\; \varphi} & {{- \sin}\; \beta} \\0 & 0 & 0 & 0 & {{- \sin}\; {\beta sin}\; \varphi} & {\cos \; \beta} \\0 & 0 & 0 & 0 & {\cos \; \varphi} & 0 \\0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & \overset{\_}{\cos \; \theta} & 0 & 0 \\0 & 0 & 0 & {- \overset{\_}{\sin \; \theta}} & 0 & 0\end{bmatrix}}} & (15)\end{matrix}$

Here, the symbol {right arrow over (u)} represents the process noisevector.

The discrete state equation transition matrix Φ_(k) is required for thisKalman filter analysis:

Φ_(k) =I+FΔs  (16)

where I is the identity matrix. Note Φ_(k)=I if Δs=0. This recognitionis used to process multiple cone flux observations with boring tool 20at one position. That is, fluxes measured by R1 and R2 of FIGS. 1 and 2are processed separately.

Update of error covariance matrix P at each new position also requires adiscrete covariance matrix Q_(k). It is obtained in a manner similar toΦ_(k) in terms of the continuous process noise covariance parametermatrix by Q_(k)=QΔs, where Q represents unmodelled increases in theerror covariance matrix P per rod foot. Only the diagonal coefficientsof Q are nonzero.

$\begin{matrix}{{Q_{11} = {Q_{22} = {Q_{33} = Q_{pos}}}},\frac{{ft}^{2}}{ft}} & (17) \\{{Q_{44} = {\frac{d}{ds}\left( \sigma_{\kappa}^{2} \right)}},\frac{1}{{ft}^{3}}} & (18) \\{{Q_{55} = {\frac{d}{ds}\left( \sigma_{\varphi}^{2} \right)}},\frac{{rad}^{2}}{ft}} & (19) \\{{Q_{66} = {\frac{d}{ds}\left( \sigma_{\zeta}^{2} \right)}},\frac{{rad}^{2}}{ft}} & (20)\end{matrix}$

These are empirical coefficients where, for example, Q₄₄ representspossible changes of maximum rod curvature due to changing soilconditions.

Measurements (observations) of fluxes and transmitter pitch are assumedto take place at regular intervals Δs along the drill pathcorresponding, in this example, to the drill rod length. With regard topitch orientation, a path segment pitch orientation is determined basedon at least one measured pitch value taken during the course of drillingthe length of one drill rod or any suitable path segment length. Thispitch value may be sensed, for example, during a concluding or endportion of a current drill rod while adding an additional drill rod tothe drill string. As one alternative, any number of pitch measurementscan be taken and an average thereof used as the path segment pitchorientation. An update of state variables in the Kalman filter looputilizes a measurement vector {right arrow over (z)}, an observationmatrix H and an observation covariance matrix R. Applying standardtechniques and in view of these teachings, these values be found bylinearizing flux equations and transmitter pitch about the nominal drillpath. Measurement vector {right arrow over (z)} contains the differencesbetween the measured values and estimates of flux components in globalcoordinates and pitch on the nominal drill path:

{right arrow over (z)}=(Δb _(x) ,Δb _(y) ,Δb _(z),Δφ)′  (21)

Δb _(x) =b _(x) _(m) −b _(x)*  (22)

Δb _(y) =b _(y) _(m) −b _(y)*  (23)

Δb _(z) =b _(z) _(m) −b _(z)*  (24)

Δφ=φ_(m)−φ*  (25)

where equations 22 through 25 represent differences between measuredvalues and estimates on the nominal drill path denoted as Δb_(x),Δb_(y), Δb_(z) and Δφ, respectively. Matrix H represents an ideal(noiseless) connection between measurements and state variables vector.Since four of the measured variables are included in the Kalman filterprocess and six variables are tracked along the drill path, this matrixhas four times six coefficients. The coefficients of matrix H arederivatives of measured quantities with respect to drill path variables,evaluated on the nominal drill path and may either be obtained in closedform or as finite differences.

Observation covariance matrix R has zero off-diagonal terms andvariances (square of standard deviation) of measured flux components andpitch placed on the diagonal.

Roll angle measurement errors are not accounted for in the solutionprocess since numerical simulation has shown that roll error has littleeffect on results. Furthermore, rod length measurement errors cannot beaccounted for since rod arc length s is used as independent variable ofthe rod equations.

Instead of processing all components of flux of each cone simultaneouslyas might be inferred from the measurement vector {right arrow over (z)},the method can be modified to update tracking data by processing fluxcomponents sequentially. This reduces {right arrow over (z)} to twocoefficients, representing one flux component and pitch.

Step 3: State variables and estimation errors are calculated usingKalman filter analysis which can be viewed as a predictor-corrector typeprocess. Values of state variables and estimation errors are projectedfrom the current k-th position to the (k+1)-st position (predictor step)and subsequently corrected by the filter (corrector step). The Kalmanfilter loop is designed to calculate state variables such thatestimation errors are minimized. There are several versions of theKalman filter loop available in the published literature. Examples andthe notation adopted for this disclosure can be found in the book of R.G. Brown and P. Y. C. Hwang entitled “Introduction to Random Signals andApplied Kalman Filtering”, John Wiley & Sons, 1997.

An estimate of the state vector at the (k+1)-st position as input to theKalman filter loop is

{right arrow over ({circumflex over (x)}={0}  (26)

Additional inputs to the filter loop include the matrices Φ,Q,H,R andthe vector {right arrow over (z)}. The coefficients of Q, R are keptconstant during the bore whereas Φ, H, {right arrow over (z)} areupdated at the (k+1)-st position on the nominal drill path.

Filter loop calculations are performed once for each cone and drill pathposition. Since the transmitter remains at the same position whenprocessing the next cone, Δs is set to zero before reentering the filterloop.

Parameter values at each new drill path position (at the end of eachdrill rod, in this example) are found by adding state variables tonominal drill path parameters. Estimation error standard deviations arethe square roots of the diagonal elements of error covariance matrix P.

Tracking Technique B

Tracking accuracy is further improved by incorporating measured yawangle, either β or ζ, in the Kalman filter process. Hence, technique Badds measured yaw angle to the determination process. The analysisfollows closely that of technique A. Rod equations and state variablesare the same, but the set of observation equations must be modified toaccount for measured yaw.

More specifically, if yaw angle β is measured, vector {right arrow over(z)} must be enlarged to read

{right arrow over (z)}=(Δb _(x) ,Δb _(y) ,Δb _(z),Δφ,Δβ)′  (27)

with Δβ=β_(m)−β* so as to encompass the difference between measured yawand determined yaw on the nominal drill path. Matrix H is modifiedsince, in this case, five variables are measured and six variables aretracked. Furthermore, observation covariance matrix R must be enlargedaccordingly to include the yaw angle variance σ_(β) ². Similarmodifications are made if yaw angle ζ is measured instead of β.

Tracking Technique C

This technique is a simplified form of technique B which does not employcones for flux measurements and which does not require a transmitter toemit a magnetic dipole field, as well as corresponding receivers Liketechniques A and B, technique C is also based on rod equations 3 through8 and defines state variables in a like manner. Since only transmitterpitch and yaw are measured, measurement vector {right arrow over (z)} isreduced to the following in cases where yaw angle β is measured.

{right arrow over (z)}=(Δφ,Δβ)  (28)

Δφ=φ_(m)−φ*  (29)

Δβ=β_(m)−β*  (30)

Matrices H and R are modified accordingly. Similar modifications aremade if yaw angle ζ is measured.

It should be appreciated that another version of technique C may utilizemeasured pitch without the need to measure yaw angle. Since onlytransmitter pitch is measured, measurement vector {right arrow over (z)}is reduced to the following:

{right arrow over (z)}=(Δφ)  (31)

Δφ=φ_(m)−φ*  (32)

Once again, matrices H and R are modified accordingly.

Tracking Technique D

For pure steering or alternate drilling/steering a yaw angle change canbe calculated combining rod equations 7, 8 and equation 9, as follows:

$\begin{matrix}{{\Delta \; \beta} = {{- \frac{\Delta \; \varphi}{\cos \; \varphi}}\frac{\overset{\_}{\sin \; \theta}}{\overset{\_}{\cos \; \theta}}}} & (33)\end{matrix}$

Theoretically, this equation applies if | cos θ|≠0 and |φ|≠90 deg. Inthe instance of pitch, it should be appreciated that a pitch angle of 90degrees, wherein the boring tool elongation axis is vertically oriented,is rarely seen in horizontal directional drilling applications. However,in order to achieve reliable tracking results, more restrictiveconditions should be imposed, for instance | cos θ|≧0.5 and |φ|≦60°. Inthe special case of pure steering at a constant roll angle θ_(s), thefirst condition will limit the usable roll angle range to−60°≦θ_(s)≦+60° and −120°≦θ_(s)≦+120°.

One technique for removing the roll angle limitation from equation 33resides in deriving maximum steering curvature from a previous drill rodwhere the steering motion was predominantly up or down. Curvature can becalculated from:

$\begin{matrix}{\kappa = \frac{\Delta \; \varphi}{{\overset{\_}{\cos \; \theta} \cdot \Delta}\; s}} & (34)\end{matrix}$

Subsequently, the desired yaw angle change is obtained from:

$\begin{matrix}{{\Delta \; \beta} = {{- \frac{{\kappa \cdot \Delta}\; s}{\cos \; \varphi}}\overset{\_}{\sin \; \theta}}} & (35)\end{matrix}$

It is noted that this equation applies to all roll angles but assumesthat soil conditions have not changed since data were taken for thecalculation of curvature based on equation 34.

Once yaw angle is obtained as described, drill path coordinates areobtained by integrating the first three rod equations numbered 3 through5. This latter integration is well known in drill path tracking.

Having described technique D in detail, it is appropriate at thisjuncture to note at least certain advantages over the prior art. Inparticular, this technique provides for yaw determinations basedprimarily on pitch and roll measurements. In this regard, determinationof yaw angle in the prior art has been somewhat problematic. Earlymethods such as, for example, the '062 patent described above, simplyignored yaw angle. Later methods such as, for example, the '951 patentdescribed above, operated under the assumption that physicalmeasurements extending considerably beyond pitch and roll were requiredto contribute in a somewhat direct way to the determination of yaworientation. For example, magnetic flux measurements often have beenapplied with the objective of determining yaw orientation. While theseprior art methods were highly effective in view of the then-existingstate of the art, the present invention completely sweeps aside thisassumption. As is clearly shown by technique D, a boring tool can betracked in an effective manner based on pitch and roll measurementsalone. The only other required parameters are readily measurable andrelate to the drill string itself. Specifically, these parameters areidentified as maximum curvature of the drill string in the drillingregion and the length of the drill string.

Still considering the advantages of technique D, roll orientationparameter determinations may be performed over a segment of the drillingpath at a plurality of equally spaced apart positions, as set forthabove in the discussions relating to equations 1 and 2. Any additionalmeasured inputs serve to further enhance position and orientationdeterminations. For example, such additional inputs include magneticflux readings and yaw measurements. Accordingly, it is recognized thattechnique D is fundamental to all of the techniques described herein, aswill be further described immediately hereinafter.

The present invention recognizes that yaw determinations may be basedupon roll and pitch determinations in conjunction with known extensionof the drill string. In a fundamental sense, it is recognized that bymeasuring extension of the drill string into the ground in combinationwith measurement of pitch and roll, a resulting position of the boringtool can be predicted. In other words, for a given extension of thedrill rod into the ground at a given, averaged roll orientation duringthe extension and at a given pitch orientation, some determinableportion of the extension contributes to a change in vertical position,thereby influencing pitch orientation, while another determinableportion of the extension contributes to a change in horizontal position,thereby influencing yaw orientation.

Techniques A-D, including any modified forms thereof, may be viewed in ahierarchical fashion having technique D as an underlying foundation.Technique C, executed without measured yaw orientation, builds furtherby providing a highly advantageous position and orientation trackingframework based on measured roll and pitch orientation values whichaccounts for measurement errors using a Kalman filter approach, althoughany suitable technique may be employed for the purpose of dealing withmeasurement errors, as described above. In this regard, any measurementerror compensation technique that is adopted should be readilyexpandable to account for measurement errors in parameters that aremeasured in the context of techniques A-C including any modified oralternative forms of these techniques. As a first example, technique Cis alternatively configurable for using measured yaw angle and toaccount for yaw orientation measurement error, as described above.

Moving up in hierarchy from technique C is technique A. This lattertechnique adds electromagnetic locating field measurements to theoverall process, while accounting for flux measurement errors, butwithout utilizing measured yaw angle. Method B tops the hierarchy byfurther taking into account measured yaw orientation, including anymeasurement error therein.

Having described techniques A-D in detail above, numerical simulationsusing techniques A and D will now be described. In this regard,attention is immediately directed to FIGS. 5 a-d wherein FIG. 5 a showsa drilling region 100, in plan view using an x,y coordinate system,having four cones C1, C2, C3 and C4 located at the illustratedtriangular shaped symbols. Table 2 gives x and y coordinates for each ofthe cones.

TABLE 2 (see FIG. 5a) Cone number x coordinate (ft) y coordinate (ft) zcoordinate (ft) 1 80 −10 12 2 160 −50 6 3 240 −1 6 4 275 −180 6

A drill path 102, shown in FIGS. 5 a and 5 c, has been used to validatetechnique A. The plan view of FIG. 5 a resembles a large quarter-circleextending nearly three hundred feet out and another three hundred feetto the right, as seen in the drilling direction of the figure at drillbegin (i.e., from x=0, y=0). FIG. 5 c is an elevational view of drillpath 102 showing depth of the boring tool plotted against arc length s.The maximum depth of path 102 is about 7.5 ft below a horizontal planepassing through the origin of the global coordinate system. Exactposition coordinates, pitch, yaw and rod bend radius are generated witha minimum rod bending radius of 200 ft and a set of steering/drillingparameters sin θ, cos θ that were also used in tracking simulations.

It is noted that FIGS. 5 a, 5 c and 5 g show predicted tracking dataobtained from “measured” or “synthesized” transmitter pitch, as will bedescribed below with reference to FIG. 5 e, and from the fluxes measuredat the four cones placed along the drill path, plotted against s and asthe difference between predicted and exact coordinates, whilecorresponding FIGS. 5 b, 5 d, 5 f and 5 h show errors in the predicteddata of interest. For example, FIG. 5 a shows the predicted drill pathin the xy plane as a series of “+”, symbols while FIG. 5 b shows a plotof x error as a solid line and a plot of y error as a broken line.Fluxes and pitch are “measured” at every four foot increment of rodlength. These “measured” data were obtained by adding white noise with 1sigma values of 0.5 deg to exact pitch and 2×10⁻⁶ to exact fluxes perunit dipole strength, respectively.

FIG. 5 c illustrates the exact z component of assumed drill path 102 asa solid line and shows the depth of predicted drill path points as aseries of “+” symbols. Referring to FIG. 5 d, vertical drill pathposition errors, corresponding to the predicted positions of FIG. 5 c,are plotted against s.

Turning again to FIG. 5 e, exact pitch of the assumed path is plottedagainst s as a solid line. A series of “+” signs indicates predictedpitch values in relation to the assumed path. In this regard, it shouldbe appreciated that there are two types of pitch angle associated withthe present type of analysis: 1) a measured pitch obtained from a pitchsensor forming part of the boring tool and (2) a predicted pitch that isone output of the Kalman filter. Consequently, there are also two typesof pitch error shown in FIG. 5 f: (1) a measurement error, correspondingto each pitch measurement and each of which is indicated by a circlesymbol and (2) a prediction error plot which is shown as a solid linethat is influenced by the introduced pitch measurement error.

FIG. 5 g illustrates exact yaw for the assumed path plotted against shaving predicted yaw values denoted by a series of “+” symbols. FIG. 5 hillustrates a corresponding plot of yaw error, in degrees, against s.

FIGS. 6 a and 6 b provide error estimates for drill path 102, defined as1 standard deviation or 1 sigma, obtained from exact cone fluxes andpitch and representing errors in position coordinates (FIG. 6 a), aswell as pitch and yaw angles (FIG. 6 b) that can be expected usingmeasured fluxes and pitch, which are used as input for the presenttracking technique simulation. Errors seen in tracking results of FIGS.5 b, 5 d, 5 f and 5 h agree well with estimated errors shown in FIGS. 6a and 6 b.

It should be emphasized that the purpose of the foregoing simulation isto demonstrate the remarkably powerful tracking capability of techniqueA. It is not intended to indicate what level of absolute drillingaccuracy this method can provide. If needed, several expedients areavailable to even further improve the accuracy achieved in this example.These expedients include, for example, increasing transmitter signalstrength to lower the noise level per unit dipole strength, the use of atransmitter with a more accurate pitch sensor, and/or the placement ofadditional cones along the drill path.

Attention is now directed to FIGS. 7 a-7 d for purposes of describing anumerical simulation of technique D. FIG. 7 a illustrates “measured”pitch and roll angles as generated for an assumed drill path 120 that isshown in FIGS. 7 b and 7 d and plotted in the xy plane and xz plane,respectively. Corresponding assumed pitch 122 and assumed roll angle 124are shown in FIG. 7 a and plotted against the x axis. Thus, for theassumed drill path, exact pitch and roll angles, as well as exactposition coordinates are known. Predicted values for yaw angle and xyzcoordinate positions are shown using a “+” symbol in proximity to eachplot in FIGS. 7 b, 7 c, 7 d.

Turning to FIG. 7 a, “measured” angles are obtained by adding whitenoise to the exact values with a 1 standard deviation error of 0.5degrees for pitch and 3 degrees for roll, respectively. FIG. 7 c showsyaw angles predicted with equation 33 plotted against x. The exact yawangle for the assumed path is shown by a solid line indicated byreference number 130 while calculated positions are shown as “+” symbolsproximate to the exact yaw plot. FIG. 7 d also uses “+” symbols toindicate predicted coordinates in the xz plane, also showing a solidline plot 132 of exact z axis depth against the x axis in relation tothe predicted z axis depths. It is readily evident, as seen in FIGS. 7 athrough 7 d, that the drill path predicted with “measured” pitch androll and calculated yaw, as input, follows the known exact drill path.Thus, tracking accuracy may be acceptable for some tracking tasks over adistance of 100 feet or so, especially in light of the large assumedroll angle measurement error used in this simulation. It is worthwhileto notice that the predicted drill path does not reflect the randomvariations of the “measured” input data due to the smoothing effect ofnumerical integration. It is submitted that the accuracy which isprovided by technique D, using only roll and pitch measurements, has notbeen attained by the prior art.

Turning to FIG. 8, a flow diagram, generally indicated by the referencenumber 200, illustrates the steps which form technique B and whichsubsumes the steps of all described techniques. In step 202, initialvalues of error covariance matrix and maximum curvature are specified.In addition, cone position coordinates are input as well as empiricaldata for the observation covariance matrix and the discrete processnoise covariance matrix. In step 204, for each position k on thedrillpath, drillpath variables comprising nominal drillpath positioncoordinates, curvature, pitch and yaw, are measured wherein a series ofyaw measurements are used as taken along Δs. In step 206, nominal drillpath coordinates are calculated along with cone fluxes for thetransmitter on the nominal drill path. In step 208, the state variablesvector {right arrow over (x)} and error matrix P are projected to thenew or next k position. State equation matrix Φ, measurement vector andobservation matrix H are calculated. The Kalman filter is executed instep 210 for each cone at one k position of the drillhead. Step 212determines if the Kalman filter loop need be repeated with data from anadditional cone and, if so, step 210 is repeated. In this regard, theimbedded Kalman filter loop is entered separately for each cone.Otherwise, execution passes to step 214 wherein drillpath variables aredetermined. Step 216 determines if the process is to be repeated for anext one of the k positions so as to repeat the process beginning withstep 204. Upon completion of the final k position, stop step 218 isentered.

Inasmuch as the techniques and associated method disclosed herein may beprovided in a variety of different configurations and modified in anunlimited number of different ways, it should be understood that thepresent invention may be embodied in many other specific forms withoutdeparting from the spirit or scope of the invention. Therefore, thepresent examples and methods are to be considered as illustrative andnot restrictive, and the invention is not to be limited to the detailsgiven herein, but may be modified within the scope of the appendedclaims.

What is claimed is:
 1. In a system for tracking a boring tool whichmoves in an underground region having an overall orientation that ischaracterized by a pitch orientation, a roll orientation and a yaworientation and said boring tool is steerable underground in the regionusing said roll orientation, said boring tool being configured foradvancing in a straight ahead mode during a continuous roll and furtherbeing configured for advancing in a steering mode by moving the boringtool at a fixed roll orientation, a method comprising: establishing aseries of spaced apart positions as the boring tool is advanced across asegment of an overall path taken by the boring tool in said region andwhich positions are separated by an at least generally equal increment;measuring a series of incremental roll positions, corresponding to saidseries of positions; and based on the incremental roll positions,selecting an operational status of the boring tool over said segment asone of the straight ahead mode, the steering mode and a mixed mode whichincludes the straight ahead mode and the steering mode.
 2. The method ofclaim 1, further comprising: as part of said selecting, determining anaveraged sine value and an averaged cosine value as averaged sums of aseries of sine values and a series of cosine values, respectively, forsaid series of incremental roll positions and establishing theoperational status based on the averaged sine value and the averagedcosine value.
 3. The method of claim 1, further comprising: selectingthe operational status based on evaluating a steering parameter that isexpressed as:$\sqrt{\overset{\_}{\cos \; \theta^{2}} + \overset{\_}{\sin \; \theta^{2}}}$where θ is the roll angle, cos θ is an averaged cosine value that isdetermined as a sum of a series of cosine values of the measured rollorientation corresponding to the series of incremental roll positions,sin θ is an averaged sine value that is determined as a sum of a seriesof sine values of the measured roll orientation corresponding to theseries of incremental roll positions, and where an evaluated value ofzero for the steering parameter establishes that the straight ahead modeis used exclusively over the path segment, a value of one for thesteering parameter establishes that the steering mode is usedexclusively over the path segment and any intermediate value betweenzero and one establishes that the mixed mode is in use over the pathsegment.
 4. The method of claim 2 further comprising: for advancing theboring tool over the segment at least using the steering mode,determining a segment pitch orientation based on at least one measuredpitch orientation of the boring tool along the segment; and establishingan incremental change in a yaw orientation of the boring tool based onthe averaged cosine value, the averaged sine value, the pitchorientation of the boring tool and an incremental change in the pitchorientation along the segment.
 5. The method of claim 4 whereinestablishing the incremental change in the yaw orientation is based onthe expression:${\Delta \; \beta} = {{- \frac{\Delta \; \varphi}{\cos \; \varphi}}\frac{\overset{\_}{\sin \; \theta}}{\overset{\_}{\cos \; \theta}}}$where Δβ is the incremental change in the yaw orientation, φ is thepitch orientation of the boring tool and Δφ is the incremental change inthe pitch orientation along the segment.
 6. The method of claim 1,further comprising: establishing a maximum drill string curvatureavailable in said steering mode within said region; as part of advancingthe boring tool over the path segment in said region, using at least oneof the straight ahead mode and the steering mode; establishing anaveraged roll characteristic for movement of the boring tool along saidpath segment based on the incremental roll positions; determining asegment pitch orientation based on at least one measured pitchorientation of said boring tool along said segment; and using themaximum drill string curvature in combination with the averaged rollcharacteristic and the path segment pitch orientation, determining saidyaw orientation of the boring tool.
 7. The method of claim 6 whereindetermining the yaw orientation includes calculating an incrementalchange in yaw orientation, Δβ, based on:${\Delta \; \beta} = {{- \frac{{\kappa \cdot \Delta}\; s}{\cos \; \varphi}}\overset{\_}{\sin \; \theta}}$where κ is the maximum drill string curvature, Δs is a length of thesegment, φ is the segment pitch orientation and sin θ is an averagedcosine value that is determined as a sum of a series of cosine values ofthe measured roll orientation corresponding to the series of incrementalroll positions and serving as the averaged roll characteristic.
 8. Themethod of claim 7 further comprising determining the maximum drillstring curvature based on:$\kappa = \frac{\Delta \; \varphi}{{\overset{\_}{\cos \; \theta} \cdot \Delta}\; s}$where Δφ is an incremental change in the pitch orientation over thelength Δs, and cos θ is an averaged cosine value that is determined as asum of a series of cosine values of the measured roll orientationcorresponding to the series of incremental roll positions.